Nonlinear equations with natural growth terms and measure data.
We prove the existence of solutions of the unilateral problem for equations of the type Au - divϕ(u) = μ in Orlicz spaces, where A is a Leray-Lions operator defined on , and .
Some conditions for the existence and uniqueness of solutions of the nonlocal elliptic problem , are given.
The non-local Gel’fand problem, with Dirichlet boundary condition, is studied on an n-dimensional bounded domain Ω. If it is star-shaped, then we have an upper bound of λ for the existence of the solution. We also have infinitely many bendings in λ of the connected component of the solution set in λ,v if Ω is a ball and 3 ≤ n ≤ 9.
In this note we give an overview of recent results in the theory of electrorheological fluids and the theory of function spaces with variable exponents. Moreover, we present a detailed and self-contained exposition of shifted -functions that are used in the studies of generalized Newtonian fluids and problems with -structure.
This note is concerned with the recent paper "Non-topological N-vortex condensates for the self-dual Chern-Simons theory" by M. Nolasco. Modifying her arguments and statements, we show that the existence of "non-topological" multi-vortex condensates follows when the number of prescribed vortex points is greater than or equal to 2.
Using a recent critical point theorem due to Bonanno, the existence of a non-trivial solution for a class of systems of n fourth-order partial differential equations with Navier boundary conditions is established.
Models introduced by R. F. Streater describe the evolution of the density and temperature of a cloud of self-gravitating particles. We study nonuniqueness of steady states in annular domains in , d ≥ 2.